Skip to main content
SpringerLink
Log in

The sets of abstract trigonometric series induced by Lp

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

The constructive character of Lp and the rate-summability provide starting-points for the present investigation. This paper considers the constructive spaces LTλ p and \(\mathcal{L}_{T\lambda }^p\). The constructive character of these spaces is determined by the rate λ. By appropriate λ’s the LTλ p forms the subspaces of Lp and the \(\mathcal{L}_{T\lambda }^p\) forms the abstract sets of Fourier-Schwartz series. The constructive spaces preserve (in generalized form) the structural properties of Lp. It is used to develop the G. Goes method of complementary spaces and to consider the multipliers between different constructive spaces.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Butzer P.L., Scherer K., On the fundamental approximation theorems of D. Jackson, S. N. Berstein and theorems of M. Zamansky and S. B. Steĉkin. Aequationes math., 1969, 3, 170–185.

    Article  MathSciNet  MATH  Google Scholar 

  2. Edwards R. E., Fourier Series. A modern introduction. Vol.I and II., Holt, Rinehart and Winston, New York, etc., 1967.

    Google Scholar 

  3. Goes G., BK-Räume und Matrixtransformationen für Fourierkoeffizienten. Math. Z., 1959, 70, 345–371.

    Article  MathSciNet  MATH  Google Scholar 

  4. Goes G., Komplementräre Fourierkoeffizientenräume und Multiplikatoren. Math. Ann., 1959, 137, 371–384.

    Article  MathSciNet  MATH  Google Scholar 

  5. Kangro G., Summability factors for the series λ-bounded by the methods of Riez and Cesàro. Tartu Ülik. Toimetised, 1971, 277, 136–154. (in Russian)

  6. Kralik D., Elementary method of the theory of series in approximation theory. Math. Lapok., 1980,28, 27–33.

    MathSciNet  MATH  Google Scholar 

  7. Sikk J., Complementary spaces with rapidity of Fourier coefficients. Tartu Ülik. Toimetised, 1975, 355, 222–235. (in Russian)

    MathSciNet  Google Scholar 

  8. Sikk J., Matrix mappings for rate-spaces and K-multipliers in the theory summability. Acta et Comm. Univ. Tartuensis, 1989, 846, 118–128.

    MathSciNet  Google Scholar 

  9. Sikk J., The rate-spaces m(λ), c(λ), c0(λ) and ℓp(λ) of sequences. Acta et Comm. Univ. Tartuensis, 1994, 970, 87–96.

    MathSciNet  Google Scholar 

  10. Tõnnov M., Summability factors, Fourier coefficients and multiplicators. Tartu Ülik. Toimetised, 1966, 192, 82–97. (in Russian)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Estonian Agricultural University, Kreutzwaldi str. 5, EE-51014, Tartu, Estonia

    Jaak Sikk

Authors
  1. Jaak Sikk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jaak Sikk.

Additional information

This work was supported by Estonian Science Foundation, grants 2416 and 3991.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sikk, J. The sets of abstract trigonometric series induced by Lp . Results. Math. 38, 152–165 (2000). https://doi.org/10.1007/BF03322438

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03322438

1991 Mathematics Subject Classification

Key words and phrases

Search

Navigation